Average Error: 28.6 → 28.7
Time: 38.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\mathsf{fma}\left(y, y + a, b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\mathsf{fma}\left(y, y + a, b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3675327 = x;
        double r3675328 = y;
        double r3675329 = r3675327 * r3675328;
        double r3675330 = z;
        double r3675331 = r3675329 + r3675330;
        double r3675332 = r3675331 * r3675328;
        double r3675333 = 27464.7644705;
        double r3675334 = r3675332 + r3675333;
        double r3675335 = r3675334 * r3675328;
        double r3675336 = 230661.510616;
        double r3675337 = r3675335 + r3675336;
        double r3675338 = r3675337 * r3675328;
        double r3675339 = t;
        double r3675340 = r3675338 + r3675339;
        double r3675341 = a;
        double r3675342 = r3675328 + r3675341;
        double r3675343 = r3675342 * r3675328;
        double r3675344 = b;
        double r3675345 = r3675343 + r3675344;
        double r3675346 = r3675345 * r3675328;
        double r3675347 = c;
        double r3675348 = r3675346 + r3675347;
        double r3675349 = r3675348 * r3675328;
        double r3675350 = i;
        double r3675351 = r3675349 + r3675350;
        double r3675352 = r3675340 / r3675351;
        return r3675352;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3675353 = t;
        double r3675354 = y;
        double r3675355 = z;
        double r3675356 = x;
        double r3675357 = r3675356 * r3675354;
        double r3675358 = r3675355 + r3675357;
        double r3675359 = r3675354 * r3675358;
        double r3675360 = 27464.7644705;
        double r3675361 = r3675359 + r3675360;
        double r3675362 = r3675354 * r3675361;
        double r3675363 = 230661.510616;
        double r3675364 = r3675362 + r3675363;
        double r3675365 = r3675364 * r3675354;
        double r3675366 = r3675353 + r3675365;
        double r3675367 = i;
        double r3675368 = c;
        double r3675369 = a;
        double r3675370 = r3675354 + r3675369;
        double r3675371 = b;
        double r3675372 = fma(r3675354, r3675370, r3675371);
        double r3675373 = cbrt(r3675354);
        double r3675374 = r3675373 * r3675373;
        double r3675375 = r3675372 * r3675374;
        double r3675376 = r3675375 * r3675373;
        double r3675377 = r3675368 + r3675376;
        double r3675378 = r3675354 * r3675377;
        double r3675379 = r3675367 + r3675378;
        double r3675380 = r3675366 / r3675379;
        return r3675380;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Derivation

  1. Initial program 28.6

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt28.7

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + c\right) \cdot y + i}\]

  4. Applied associate-*r*28.7

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}} + c\right) \cdot y + i}\]

  5. Simplified28.7

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{\left(\mathsf{fma}\left(y, y + a, b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right)} \cdot \sqrt[3]{y} + c\right) \cdot y + i}\]

  6. Final simplification28.7

    \[\leadsto \frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\mathsf{fma}\left(y, y + a, b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right)}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))